What is stability?Edit
In short, stability makes it harder for ships to be destroyed. The stack can take x% damage before a ship is destroyed. Stability is what percent of the total hull strength (durability) that a stack must take to the ship hull (not shields), which will destroy one ship. For example, at 400% stability, if you deal 10,000 damage to a stack of ships with 1,000 structure, you will destroy only 2 ships. (2 ships x 1000 x 400% = 8000. 3 ships require 12,000 damage, so only 2 ships are destroyed. NOTE: a stack can only take 100% of its total durability, and then it is destroyed. Stability keeps more ships in a stack longer, allowing repair or to fight back. This means at 400% stability, you will keep 75% or more of your ships, or lose them all.
The ship stability of a ship will improve the endurance of a ship and will help you last longer during the fight...so it is basically giving steroids to your ships.
What gives ships stability?Edit
Stability is gained from the ship hull selection (usually 40-60% bonus), from a few modules, such as Gravity Maintenance Facility,Ship Reinforcement Facility, Copernicus Gyroscope, Daedalus Control System, Icarus Control System, and from the Ship Defense Science technology tree (60%). Daedalus at full tech has a 30% chance to increase 100% per attack. Stability can also be increased via implanting certain gems and bionic chips into the commander that is controlling the fleet.